Actually it is 2*N*e. Of course the signal you see depends on which charge you collect. If you only collect electrons you will see N*e, even though 2*N*e was produced.

An interesting example of this is the following.

While characterizing Silicon Photomultipliers (SiPM) I measured the photon detection efficiency (PDE). The canonical method, used by everyone till that moment, was to illuminate the photosensor with a monochromatic light source, inside an integrating sphere where a calibrated photodiode is installed. By measuring the photocurrent (after subtracting the dark noise current) and normalizing to the calibrated diode one gets the PDE. This is wrong, for two reasons.

1) With this procedure one includes also the cross-talk in the SiPM.

2) The overall photocurrent is due to electrons AND holes.

I employed a new method, i.e. by counting the single photons with the SiPM and, on top of a better control of the cross-talk, I got the expected result for the PDE (1/2 of what measured with the photocurrent).

The number of interactions is N. You produce two charges per interaction, so the number of charges is 2N*e, you produce holes and electrons. If you take into account the sign of charges, the amount of charge of course is zero.

Actually it is 2*N*e. Of course the signal you see depends on which charge you collect. If you only collect electrons you will see N*e, even though 2*N*e was produced.

An interesting example of this is the following.

While characterizing Silicon Photomultipliers (SiPM) I measured the photon detection efficiency (PDE). The canonical method, used by everyone till that moment, was to illuminate the photosensor with a monochromatic light source, inside an integrating sphere where a calibrated photodiode is installed. By measuring the photocurrent (after subtracting the dark noise current) and normalizing to the calibrated diode one gets the PDE. This is wrong, for two reasons.

1) With this procedure one includes also the cross-talk in the SiPM.

2) The overall photocurrent is due to electrons AND holes.

I employed a new method, i.e. by counting the single photons with the SiPM and, on top of a better control of the cross-talk, I got the expected result for the PDE (1/2 of what measured with the photocurrent).

In an electrolyte the charge carriers are ions of opposite signs. There are two charge carriers. Nevertheless, when a battery is charged we refer to the stored electrons as Amp-h of charge. The purpose of the battery is to supply electrons to a circuit.

The same situation exists for a semiconductor radiation detector. There are two charge carriers, electrons and holes. The output to a circuit is electrons. With an electrolyte part of the process must be described by both charge carriers, while the product is neither charge carrier. The semiconductor process is described with electrons and holes. The product is one of the carriers. The total charge carriers produced in a semiconductor process is 2N, but the product is N. Which number you use depends upon what you are describing.

in order to talk about charge you must collect it on the electrodes in simplest case of parallel plates d microns (etc.) apart - you e-h pair will split and drift in opposite directions

if both arrive to the electrodes the collected charge will be equal to 1.62 x 10-19 C so one electron .....

if one or other or both are trapped before reaching the collecting electrodes your collected charge will be proportional to the drift path (where complete drift gives 1e)....schockley-ramo theorem and more general gunn's theory (induced currents in any geometry and number of electrodes)

Dear paolo,

Thanks for the clarification. But still I have a little confusion regarding the practical usage of this concept in front end electronics. Suppose for the amount of charge generated inside the semiconductor I get a Charge sensitive preamplifier output pulse height as say V (volts) then is V=Ne/Cf or V=2Ne/Cf. ? (Cf= feed back capacitance of the charge amplifier?)

well just simplest explanation .. in fact there are no holes, so that electrons hoping to fill in the hole, in valence band - thus in fact it's only electrons current moving one direction depending on the applied E .... it will be always N and not 2N when using charge sensitive electronics and collecting all the charges..

V=[CCE(charge collection efficiency if full=1)*N(number of e-h pairs)*q]/Cf

http://czt-lab.engin.umich.edu/journals/Zhong%20He/ShockleyRamo.pdf

@Prasanna

V=Ne/Cf.

There is a free Silvaco webinar ¨Simulating Total Dose, Prompt Dose, Damaging Fluence and SEU using TCAD¨ on 17th February.

http://www.silvaco.com/webinar/tacd_simulation_for_total_dose.html

There is a free Silvaco webinar ¨Simulating Total Dose, Prompt Dose, Damaging Fluence and SEU using TCAD¨ on 17th February.

http://www.silvaco.com/webinar/tacd_simulation_for_total_dose.html

dear paolo,

 Thanks for the clarification. But I wonder would it be practically possible to collect only one type of charge ( either electrons or holes) when the current that flows though the detector is a combination of both?

Of course it is possible! You just connect one electrode to ground and the other one to your charge integrating device (pre)amplifier. Half of the charge will flow undetected toward ground. If you use a differential (pre)amplifier, instead, you will collect all of the charge. :-)

Oh my god! I have been unnecessarily struggling with this charge collection concept for a long time. Thanks a lot Paolo, for your answer made me SIT and THINK and my STRUGGLES came to an END. Actually I made a wrong assumption in my mind of signal current flow inside a reverse biased detector being similar to current flow inside a normal (undoped) semiconductor block. You can imagine what kind of confusions that would lead me to. Thank you once again. :-)